Montshire Minute: Game Theory

Originally aired during the week of November 13, 2000

Monday

Imagine that you and your best friend become partners in crime. The police don't have solid proof, so the two of you get put in separate cells. The DA walks in and says: "I'll make you a deal. Blame your partner for the crime, and he goes to jail and you can walk. But the catch is: I'm making the same offer to your partner." If you both keep your mouths shut, you'll each get only a small jail sentence. If you rat on each other, both of you will do longer time. However, if you betray your partner and he keeps his mouth shut, you'll be scott free (except for a guilty conscience, because he'll end up doing a big time jail sentence). You are seated on the horns of a dilemma, a very uncomfortable place to be. To be exact, this is called the Prisoner's Dilemma, and we all find ourselves making difficult choices like this one during our lives.

Tuesday

Think its hard to win a Nobel prize? Well, a few years ago, three college professors shared the Nobel prize in economics "for pioneering analysis of equilibrium in the theory of non-cooperative games." In other words, they played a lot of monopoly. I'm kidding, I'm kidding! Game theory is taken very seriously by researchers who are interested in helping us all make rational decisions. Game theory was invented by John Von Neumann, who also helped design the first digital computer. For the purposes of his research, Von Neumann, assumes everything we do is a game, and that every game has a single best strategy for each player. Even a complex game like chess has to have a single best strategy that produces a winner with the least amount of moves. The simplest game is the "zero-sum" game, which means one player wins and one player loses. Most two-team or two-person sports are zero sum games.

Wednesday

Game theory has been used by researchers to simulate the most dangerous game of all: nuclear war. But since a nuclear war is something no one can really win, the question becomes: What's the best strategy for not fighting? So, as Bob Berger relates in his book Beating Murphy's Law, game theorists developed the idea of the non-zero sum game, where each player is still competing, but for a mutual benefit. In other words: compromise. In the Prisoners' Dilemma game, each of the two partners in crime (lets say its those two love birds Bonnie and Clyde) is offered a deal: rat on your partner and you'll go free, while your partner does time in jail. That's a pretty tempting offer. But if they both rat on each other, they both end up in the slammer. If they remain true to each other, they do a shorter jail sentence, after which they end up in each others arms again.

Thursday

Imagine you're in a subway station where the turnstiles aren't working. There's a little wooden box next to each turnstile where commuters can put their tokens. It's sort of run on the honor system. Your choice is to cooperate and drop a token into the box. Or, you could blow it off and take a free ride. So, what's the big deal? If you don't put your token in, who's going to know? According to game theory, getting something for nothing is "optimizing" your gains. Of course, if everyone thought that way, then the whole train system would be bankrupt in a hurry. The principle of suboptimization says that gaining in the short run often means losing in the long run. In this case, everybody running around trying to optimize their gains ends up loosing their means of getting to work in the morning. Maybe suboptimization is just a fancy way of saying: crime doesn't pay - at least in the long run.

Friday

In the mid-1600's, a French nobleman named Chevalier de Mere was winning big with a dice game: the object was to roll a one in four tries. He wanted to figure out if the odds were really with him, so he asked mathematician Blaise Pascal for help. Pascal dashed off his answer and sent it to de Mere. And - zut alors! - as they say in France, Pascal had invented probability theory (and if he'd known it, the city of Las Vegas). Even if we don't play games of chance, we all assess the risk involved in our daily activities. Let's say we really want to go shopping at a particular store where there's a big fire sale. But it's snowing outside, and the roads are getting slippery. So we weigh the advantages of getting a good deal at the store against the chance of sliding into a snow bank, after which you might be looking for a good deal at an auto bodyshop. Tough choices!